Analysis and design of reinforced concrete stepped cantilever retaining wall

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308

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Volume: 04 Issue: 02 | Feb-2015, Available @ http://www.ijret.org 46

ANALYSIS AND DESIGN OF REINFORCED CONCRETE STEPPED

CANTILEVER RETAINING WALL

S.S Patil1, A.A.R.Bagban

2

1Professor and Head, Civil Engineering Department, Walchand Insitute of Technology, Solapur, Maharashtra, India

2Post Graduate Student, Walchand Institute of Technology, Solapur, Maharashtra, India

Abstract A retaining wall is one of the most important types of retaining structures. It is extensively used in variety of situations such as

highway engineering, railway engineering, bridge engineering and irrigation engineering. Reinforced concrete retaining walls have a vertical or inclined stem cast with base slab. These are considered suitable up to a height of 6m.It resists lateral earth

pressure by cantilever action of stem, toe slab and heel slab. The tendency of wall to slide forward due to lateral earth pressure

should be investigated and a factor of safety of 1.5 shall be provided against sliding. Cantilever retaining walls are found best up

to a height of 6m.For greater heights earth pressure due to retained fill will be higher due to lever arm effect, higher moments are

produced at base, which leads to higher section for stability design as well as structural design. This proves to be an

uneconomical design. As an alternative to this, one may go for counter fort retaining wall, which demands greater base area as

well as steel. As a solution to this difficulty, a new approach that is to minimize effect of forces coming from retained fill , short

reinforced concrete members in the form of cantilever steps are cast along the stem on the retaining face. Addition of these steps

would counterbalance the locally appearing forces and will result into lesser moment and shear forces along the stem. Also it will

reduce the bending action that is pressure below the base.

The objectives of the study are

1) To reduce the stresses on the retaining face of the cantilever retaining wall, it is proposed to introduce reinforced concrete

steps along the stem.

2) Decide the most economical location of step along length and also along height of wall from number of trials.

3) Decide cross section of the R. C. step as per the stresses due to frictional forces in step.

4) Stability analysis of Cantilever retaining wall with steps for unit width will be done. Check for minimum and maximum stresses

will be observed. 5) Cost comparison shall be carried out for these three different alternatives to give most economical retaining wall type.

Keywords: Mechanism of step, Finalization of Step location, Stabilizing frictional force, Concrete quantity, Steel

reinforcement and Cost Comparison of Counter fort and Stepped Cantilever retaining wall.

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1. INTRODUCTION

A retaining wall is one of the most important types of soil

retaining structures. The primary purpose of retaining wall is

to retain earth or other material at or near vertical position. It

is extensively used in variety of situations such as highway

engineering, railway engineering, bridge engineering, dock and harbor engineering, irrigation engineering, land

reclamation and coastal engineering etc. Reinforced concrete

retaining walls have a vertical or inclined stem cast

monolithic with a base slab. These are considered suitable

up to a height of 6m. It resists the lateral earth pressure by

cantilever action of the stem, toe slab and heel slab.

Necessary reinforcements are provided to take care of the

flexural stresses. The tendency of the wall to slide forward

due to lateral earth pressure should be investigated and if a

factor of safety is insufficient, a shear key should be

designed to prevent lateral movement of the structure.

1.1 Cantilever Retaining Walls

These walls are made of reinforced cement concrete. It

consists of a thin stem and a base slab cast monolithically.

This type of wall is found to be economical up to a height 6

to 8m.

Fig - 1


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1.2 Counter fort Retaining Walls

These walls have thin vertical slabs, known as counter forts,

spaced across vertical stem at regular intervals. The counter

forts tie the vertical stem with the base slab. Thus the

vertical stem and the base slab span between the counter

forts. The purpose of providing the counter forts is to reduce

the shear force and bending moments in the vertical stem

and the base slab. The counter fort retaining walls are economical for a height more than 6 to 8m.

Fig - 2

2. ANALYSIS OF RETAINING WALLS

2.1 Cantilever retaining wall

A) Stability:

Figure 3 shows a cantilever retaining wall subjected to

following forces:

Fig - 3: Mechanism of Cantilever Retaining Wall

Weight W1 of the stem

Weight W2 of the base slab

Weight W3 of the column of soil supported on heel

slab

Weight W4 of the soil supported on toe slab

Horizontal force Pa equal to active earth pressure acting at H/3 above base slab.

B) Modes of Failure of a Retaining Wall:

Overturning about A

The most hazardous mode of failure of retaining wall is

due to overturning because of unbalanced moments.

Here, a minimum factor of safety is used.

Sliding:

The horizontal force tends to slide the stem and wall

away from fill. The tendency to resist this is achieved

by the friction at the base. Here, if the wall is found to

unsafe against sliding, shear key below the base is provided. Such a key develops passive pressure which

resists completely the sliding tendency of wall. A factor

of safety of 1.5 is used against sliding.

Bending Failure

The stem AB will bend as cantilever so that tensile face

will be towards the soil face in case if there is no

backfill, where as tensile face will be towards the water

face in case there is backfill. The critical section will be

at E and B, where crack may occur at if it is not

properly reinforced. The soil side slab will have net pressure acting downwards, and will bent as a cantilever

having tensile face at top for retaining wall, at the same

time the heel slab will be subjected to net upward

pressure causing tensile face at bottom. The thickness of

stem, toe slab, and heel slab must be sufficient to

withstand compressive stresses due to bending also; the

stem thickness must be check for uncracked section.

2.2 Design Principal of Cantilever Retaining Wall

The various dimensions of wall are so proportioned that the

various failure criteria discussed above are taken care of.

The design of wall consist of the fixation of base width,

design of stem, design of toe slab, design of heel slab.

A) Fixation of Base Width:

The base width of wall is so chosen that the resultant of

forces remain within middle third of base slab, the uplift

pressure is zero at heel slab side also it should be safe from

consideration of sliding.

B) Design of Stem:

The vertical stem is designed as cantilever for triangular

loading with Kaγh as base of triangle h as height of it. The

main reinforcement is provided at 0.3 % of the area of cross

section along the length of wall.


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C) Design of Toe Slab:

It is also design as a cantilever beam or slab. The main

reinforcement is provided at lower face or bottom side as

upward soil pressure load is acting on that face. Thickness is

checked for maximum cantilever moment and deflection

criterion.

D) Design of Heel Slab:

It is also design as a cantilever beam or slab. The main

reinforcement is provided at the upper face or top side of heel slab as active load is acting there in form of overburden

pressure. The design reinforcement for effective moment

due to upward soil pressure should also provide at bottom

side of heel slab. The thickness is checked for maximum

cantilever moment and deflection criterion for cantilever

action.

2.3 Analysis of Counter-Fort Retaining Wall:

The counter forts support both the vertical stem as well as

base slab. Design principles for various component parts are

discussed below in brief. The same criterion is adopted for

fixing the base width as cantilever retaining wall.

A) Design of stem

Unlike the stem of cantilever retaining wall, the stem of counter fort retaining wall acts as a continuous slab

supported on counters forts. Due to varying pressure over

the height of stern, the stem slab deflects outwards and

hence main reinforcement is provided along the length of the

wall as per design conditions.

Pc - Effect of counter fort

Lc - Spacing of counter forts along length of wall

Fig - 4: Mechanism of Counter fort Retaining Wall

The reaction of the stem is taken by the counter forts, to

which it is firmly anchored. The maximum bending moment

occurs at Base. The uniformly distributed earth pressure load or water pressure load is calculated for unit height.

B) Design of Heel Slab

The action is similar that of stem. The Heel slab is subjected

to the downward load due to weight of soil and self weight,

upward load due to upward soil pressure below heel slab.

The maximum net pressure is found to act on a strip of unit

width near outer edge, since the upward soil reaction is

minimum there, the total reaction from the heel slab is

transferred to the counter forts, and this load helps to provide a balancing moment against its overturning. The

heel slab is firmly attached to the counter forts by means of

vertical ties.

C) Design of Toe Slab

The action of Heel slab is similar to that of cantilever

retaining wall.

D) Design of Counter Forts

The counter fort takes reactions, both from the stem as well

as Heel slab. As shown in fig. 4.2, the counter forts are

subjected to tensile stresses along the outer face AC of the

counter forts. The angle ABC between stem and slab has a

tendency to increase from 900, and counter forts resist this

tendency. Thus the counter fort may be considered to bend as a cantilever, fixed at BC. The counter fort acts as an

inverted T beam of varying rib depth. The maximum depth

of this T beam is at the junction B. The depth is measured

perpendicular to the sloping face AB, i.e. depth dl=BB1. At

B, This depth thus goes on decreasing towards Al where the

bending moment also decreases. The width of counter fort is

kept constant throughout its height; Main reinforcement is

provided parallel to AC The faces AB and BC of the counter

fort remain in compression. The compressive stresses on

face AB are counterbalanced by the vertical upward reaction

transferred by the slab. In addition to the main reinforcement, the counter forts are jointed firmly to the

stem and base slab by horizontal and vertical ties

respectively.

2.4: Stepped Cantilever Retaining Wall (New

Approach)

For retaining back fill of heights more than 10-11 meters.

The conventional walls like cantilever and counter fort

becomes very massive and almost uneconomical hence a

suitable modification to these walls so as to economize the

retaining wall construction. The proposed modified

alternative is ‘Stepped cantilever retaining wall’. The

general outline of concept will be clear from figure as

shown.


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P - Stabilizing frictional force

Pa - Active pressure component

L - Spacing of concrete steps along length of wall

Fig – 5: Mechanism of stepped cantilever retaining wall

The main concept in this type is supporting the high stem at

critical points indirectly by means of pulling force

developed due to surface Friction of concrete steps with

backfill. Here the effect of self weight of these steps in

stabilizing wall against active pressure is not considered as it may be negligible. Conventionally in case of sheet pile

walls, there was use of anchor rods and the concrete plates

or concrete dead man was used to develop frictional force.

In case of sheet pile wall with vertical concrete plates the

mechanism of pulling force was due to passive resistance of

soil mass bounded by height of concrete wall and in that

case the role of concrete wall was different from frictional

resistance function. In case of sheet pile walls the thickness

of stem was very small but it is continuous wall with

membrane action than beam/slab action but in this case,

these concrete steps are used as supporting mechanism for conventional cantilever wall which gives relatively less

dimensions for assumed slab beam mechanism than

conventional design approach.

A) Design Principles

Design principles for various component parts are discussed

below in brief. The procedure of analysis is same as

cantilever retaining wall but their preliminary dimensions

given will be based on load distribution assumed for actual

analysis. Like any other analysis and design this will be

Iterative (trial and error) method, the preliminary

dimensions may be approximately given as half of that for

purely cantilever wall with some exiting thumb rules.

B) Fixation of Base Width

In this case it is not necessary that the base width of wall is

so chosen that the resultant of forces remain within middle

third and the minimum (uplift) pressure at toe is zero but

these dimensions can be chosen approximately without these

checks.

C) Design of Stem

The vertical stem is designed as cantilever for triangular

loading but reinforcement will be provided from actual

modified Pressure diagram due to restoring force developed

by concrete steps. Distribution reinforcement may be

provided as per standards.

D) Design of Toe Slab

It is also designed as a cantilever slab/beam. Reinforcement

is provided at lower face. There will major reduction in depth and steel reinforcement in toe and heel slab due to

reduction in the active pressure and addition in self-weight

of wall. This will effectively economize the wall

construction. Thickness is checked for the maximum

cantilever moment.

E) Design of Heel Slab

It is also designed as a cantilever. Reinforcement is provided

at the upper face. Thickness is checked for the maximum

cantilever moment.

F) Design of Concrete Steps

The concrete steps will be placed along length at suitable

spacing L. The mechanism of friction generation is fully

dependant on overburden load i.e. depth of step from top of wall hence the step provided at more depth will give better

results. The one more effective element in friction

development is embedment length and width of step. The

overlaying or overlapping of steps and embedment in

various pressure zones like passive or rest will also be

important. These steps will act as free cantilevers spanning

from stem or somewhat like plates supported on spring or

elastic media depending upon degree of compaction of

backfill. These assumptions dominate its design or depth at

stem and free end. If steps assumed as slab strips supported

on elastic media then their depth and steel reinforcement for moment will be less than its minimum depth as per

standards and steel required for tensile forces developed due

to frictional resistance.

G) Calculation of Frictional Resistance offered by

Plate

The concrete plates are inserted in compacted backfill. They

will develop frictional force along contact planes of concrete

and soil due to overburden pressure and compaction. This

frictional force will act as indirect stabilizing force for

overturning retaining wall and will pull wall inside.


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Mechanism

The concrete plate separated from stem inserted in soil is as

shown in figure 4.

Displaced stem

Active state zone

Fig - 6: Mechanism of step

The effective frictional pressure=Coefficient of

friction x height of backfill on plate x dry density of

backfill.

Effective length of plate =Length of plate beyond

active zone.

Effective frictional force =Width of plate x effective

length of plate x 2 x Effective frictional pressure.

H) Finalization of Step Location

For actual analysis to decide location of step along length

and along height of wall is most important task as it may hamper most of assumptions. Hence the length of step

immersed in backfill was kept constant and the location of

plate along length of wall was fixed from number of trails

for stability. For finalizing the location of step along height

of wall, the number of trials is taken starting from half of

height and with interval of 500 mm. The stability analysis of

each wall is done and concrete quantity, steel reinforcement

and cost per meter are compared. The most economical wall

is selected for final comparison as alternative with other

retaining wall types. The following table shows all aspects

of stepped cantilever wall for various step heights from top

of wall. The comparison is also shown graphically by subsequent graphs for each height.

1) Stepped Retaining Wall of Height 6m:

Assumptions

1. Back fill is enough compacted.

2. Step length embedded in backfill - 3.5m

3. Step dimensions - 400 x 300 mm

Table 1: Stability analysis and cost comparison

Step from

top m.

Width of

toe slab

Width of

heel slab

Depth of

base slab

Total base

slab

Stem thick

m

At top Bottom

3 0.85 2.5 0.4 3.7 0.2 0.35

3.5 0.65 2.5 0.4 3.5 0.2 0.35

4 0.65 1.9 0.4 2.9 0.2 0.35

4.5 0.65 2.42 0.4 3.42 0.2 0.35

5 0.65 2.6 0.4 3.6 0.2 0.35

5.5 0.65 2.9 0.45 3.9 0.2 0.35

Upward soil

pressure in KN/m2

Effective

frictional force

Concrete

m3

Steel quantity

Kg/m Cost Rs/m

Pmax. Pmin.

101.7 295.2 38.21 2.305 138.26 14012.68

103.6 292 51.85 2.3625 143.3 14430.65

88 296.5 67.56 2.26 141.38 13989.34

94.7 299.1 85.36 2.6055 158.99 15955.82

101.7 296.1 105.23 2.815 176.65 17448.45

106.9 305.4 127.18 3.2675 202.55 20145.9


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Graph 1: Step location Vs concrete m3 for wall Ht. 6.0 m

Graph 2: Step location Vs steel kg for wall Ht. 6m

Graph 3: Step location Vs cost per meter for wall Ht. 6.0 m


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Assumptions




Table2: Stability analysis and cost comparison for wall ht.8m

Step from top

Width of toe slab

Width of heel slab

Depth of base slab

Total base slab

Stem thickness in m

at top

Bottom

4 1.3 3.95 0.47 5.65 0.25 0.4

4.5 1.2 3.9 0.5 5.5 0.25 0.4

5 1.1 3.85 0.5 5.35 0.25 0.4

5.5 0.95 3.9 0.45 5.25 0.25 0.4

6 1.15 3.4 0.45 5 0.25 0.45

6.5 1.25 3.2 0.45 4.9 0.25 0.45

7 1.35 3.12 0.45 4.995 0.25 0.525

7.5 1.45 3.15 0.45 5.2 0.25 0.6

Upward soil

pressure

KN/m2

Effective

frictional

force KN

Concrete

m3

Steel

quantity

Kg/m

Cost Rs/m

Pmax. Pmin.

220.63 281.53 78.91 3.9555 294.49 26507.32

213.15 299.95 100.46 4.2125 272.96 26481.03

217.81 295.3 124.61 4.3 280.63 27117.09

206.31 294.54 151.35 4.15 275.03 26351.29

197.56 295.12 180.68 4.35 320.84 29021.12

183.01 295.3 212.62 4.48 313.44 29157.92

177.32 289.68 247.15 4.96025 295.81 30080.705

172.75 286.56 284.28 5.5275 308.79 32624.22

Graph 3: Step location Vs concrete cum/m for wall Ht. 8.0 m


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Graph 4: Step location Vs steel kg/m for wall Ht. 8m



Assumptions





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Table 3: Stability analysis and cost comparison for wall hieght10m .

Step from

top m.

Width of toe

slab m

Width of heel

slab m

Depth of base

slab m

Total base

slab m

5 1.5 8.5 0.55 10.5

5.5 1.45 7.15 0.55 9.15

6 1.4 6.85 0.55 8.75

6.5 1.35 6.65 0.55 8.5

7 1.5 6.5 0.5 8.5

7.5 1.45 6.15 0.55 8.2

8 1.5 5.55 0.55 7.8

8.5 1.5 5.25 0.55 7.5

9 1.6 4.925 0.6 7.25

9.5 1.75 5.425 0.6 8

Graph 6: Step location Vs concrete cum/m for wall Ht. 8.0 m.

Graph 7: Step location Vs steel kg/m for wall Ht. 10.0 m


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Assumptions

1. Step length embedded in backfill - 6.5 M


Table 4: Stability analysis and cost comparison for wall ht.12m

Step from

top

Width of toe

slab m

Width of heel

slab m

Depth of base

slab m

Total base

slab m

6 2.1 5.9 0.75 8.65

6.5 1.9 6.6 0.75 9.15

7 1.8 6.3 0.65 8.75

7.5 1.65 6.2 0.65 8.45

8 1.5 6.35 0.65 8.45

8.5 1.4 6.1 0.65 8.2

9 1.25 5.85 0.6 7.8

9.5 1.4 5.45 0.7 7.5

10 1.51 5.09 0.7 7.25

10.5 1.6 5.6 0.65 8

11 1.7 5.2 0.65 7.8

11.5 1.8 5.225 0.7 8.1

Upward soil

pressure

KN/m2

Effective

frictional

force KN

Concretem3

Steel

quantity

Kg/m

Cost Rs/m

Pmax. Pmin.

297.29 217.93 213.27 9.4875 780.71 66776.78

295.99 229.29 252.98 10.1125 653.98 63514.89

297.01 224.59 296.07 9.1875 664.01 60708.68

299.91 240.15 342.53 9.055 602.19 57586.67

295.05 249.66 392.37 9.2925 665.24 61129.07


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286.61 260.06 445.59 9.7925 704.89 64584.02

270.77 280.76 502.18 9.405 855.36 69697.98

255.28 289.2 562.14 10 856.7 71838.1

240.75 294.08 562.14 10.075 861.16 72292.38

245.75 283.49 692.2 11.2375 810.15 74167.7

244.36 283.43 762.29 11.945 822.89 77191.77

249.26 283.24 835.76 11.85125 877.55 79214.025

Graph 9: Step location Vs concrete cum/m for wall Ht. 12m

Graph 10: Step location Vs steel kg/m for wall Ht. 12.0 m


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5) Stepped Retaining Wall of Height 15m

Assumptions

1. Step length embedded in backfill – 7.5m


Table 5: Stability analysis and cost comparison for wall ht.15m

Step

from

top m

Width

of toe

slab m

Width

of

heel

slab

m

Depth

of

base

slab

m

Total

base slab

m

Stem

thickness

in m

top

Bottom.

7.5 2.1 6.3 0.75 9.5 0.35 1.1

8 2.15 6.1 0.75 9.15 0.35 0.9

8.5 2.12 5.73 0.75 8.75 0.35 0.9

9 2.12 5.46 0.75 8.5 0.35 0.92

9.5 2 5.33 0.72 8.15 0.35 0.82

10 2 5.225 0.8 8.195 0.35 0.97

10.5 2 4.7 0.75 7.8 0.35 1.1

11 2.1 4.15 0.75 7.5 0.35 1.25

11.5 2.2 3.75 0.75 7.25 0.35 1.3

12 2.25 4.45 0.75 8 0.35 1.3

12.5 2.4 4.1 0.75 7.8 0.35 1.3

13 2.6 4.2 0.785 8.1 0.35 1.3

13.5 2.8 4.4 0.85 8.5 0.35 1.3

14 2.9 5.1 0.9 9.3 0.35 1.3

14.5 3 6.05 1 10.4 0.35 1.35


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Upward

soil

pressure

KN/m2

Effective

frictional

force KN

Concretem3

Steel

quantity

Kg/m

Cost Rs/m

Pmax. Pmin.

297.9 290.8 299.8 12.5625 928.64 83900.27

298.52 284.82 348.86 11.8625 968.68 83171.99

295.9 282.2 401 11.875 946 82240.5

291.9 275 457.9 12.09 925.5 82111.5

300 283.5 517.88 11.4255 967 81570.25

292.9 272.8 581.5 13.156 1015.9 89729.7

282 280.35 648.73 13.4625 1004 90290.75

264.5 276.8 719.6 14.425 1111 98260.5

238.88 283.5 794.12 14.925 1089 99064.5

267.8 271.9 872.19 15.9 1233 108669

234.5 286.35 954 16.1625 1167 106749.75

223.5 290.75 1040 17.0835 1064 105544.25

213 299 1128.5 18.3625 1077 110579.75

225 300 1221 19.92 1350 127770

246.25 300 1317.5 22.725 1511 144510.5

Graph 12: Step location Vs concrete cum/m for wall Ht. 15.0 m


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Graph 13: Step location Vs steel kg/m for wall Ht. 15.0m

Graph 14: Step location Vs cost per meter for wall Ht. 15.0m

3. RESULTS AND DISSCUSSIONS

Example

The example of analysis and design of stepped cantilever retaining wall are given below.

Data Assumptions

Data assumed for the stability calculation of stepped cantilever retaining wall

Free Board not necessary

The backfill is enough compacted to develop necessary friction.

Bearing Capacity of soil: 300 KN/Sq. m

Water level is much below the level of base and effect of soil moisture is ignored.

Dry density of soil: 18 KN/Cubic m.

Angle of internal friction: 300

Coefficient of friction: 0.60


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Stability is checked for sliding and overturning.

Factor of safety against sliding = 1.5

Factor of safety against overturning = 2.0

The moment and reinforcement provided for various heights are as shown in table

3.1 Counter fort Retaining wall

The structural analysis of counter fort Retaining wall is done as per routine analytical practices. Generally these walls are use for span more than 6m, but here in order to compare the results analysis and design of these counter fort retaining walls is done for

Heights 6m to 15m. The mechanism of this wall is different from cantilever wall and here Base slab is more important design

aspect.

Table 6: Dimensions of Counter fort Retaining Wall

Ht of

wall

m

Total

Base Slab

M

Width

of Toe

Slab

Width

of Heel

slab

Base

slab

Thk. M

Stem Thk. m

Top Botm.

6 3.5 0.3 3.0 0.28 0.2 0.2

8 4.25 0.5 3.45 0.35 0.3 0.3

10 5.6 1.0 4.25 0.45 0.45 0.35

12 7.75 1.25 6.05 0.5 0.45 0.45

15 10.0 2.75 6.70 0.77 0.55 0.55

Counter fort Details

Spacing 4.0 3.5 3.0 3.0 3.0

Thickness 0.3 0.375 0.4 0.45 0.55

The analysis of Base slab for wall is presented in table Here Toe slab is designed as cantilever slab spanning from stem. The

upward soil pressure will be act as major load on toe slab. But the heel slab will be designed as simply supported slab in between

two adjacent counter forts. Sometimes when toe projection is larger and if there is possibility of stress reversal in stem, the counter

forts are also provided on toe slab at that time Toe slab design will also be as heel slab design .The major load for heel slab will be

effective load from average Upward pressure and Retained soil load on heel slab.

The base slab depth is provided as per required for maximum Bending Moment while reinforcement is provided as per actual requirement for Toe and Heel slab.

Table 7: Structural Analysis of Counter-fort Retaining wall (Base slab)

Height of

wall

m

Bending moment

(KN.m) Depth of

base slab

required mm

Depth of

base slab

Provided mm Toe Heel

6 12.67 158.98 240.03 400

8 47.58 232.12 290.00 450

10 187.55 419.80 390.00 550

12 288.36 534.34 440.00 600

15 1152.18 1391.32 710.00 850

The reinforcement provided for base slab i.e. Toe slab and various locations is shown in table 8

Table 8: Design of Base slab of counter fort retaining wall

Ht. Of

wall

m.

Base slab

Thick.

Mm

Main Steel.

Toe slab Heel slab

Ast. mm2 Bar Dia. &

Spacing Ast. mm2

Bar Dia. &

Spacing


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6 400 168.73 ϕ10

@150mm 1172.70

ϕ20

@150mm

8 450 297.07 Φ12

@150mm 1538.54 ϕ20 @150mm

10 550 981.27 Φ16

@150mm 2317.76 Φ25 @150mm

12 600 1399.52 Φ20

@150mm 2724.55

Φ25

@150mm

15 850 4183.46 Φ25

@115mm 5194.55

Φ32

@150mm

The mechanism of stem of counter fort retaining wall and Cantilever retaining wall is not same. In cantilever retaining wall, stem

was acting as free cantilever with span equal height of wall while in counter fort, stem acts as simply supported slab spanning in

between two adjacent counter forts. The effective span for this will be span of counter fort along length of wall. The dimensions of

stem are reduced due to this mechanism. The bending moment of the vertical wall is maximum at the junction of stem (wall) with

Base and reduces to the zero at the top of the wall.

The moments and reinforcement provided for various heights are as shown in table 9

Table 9: Moment and Reinforcement details along length of stem for counter fort wall

Ht. of

wall

m.

Moments along

length of

stem(KNm)

Steel prov. In Vertical wall

Stem Thickness

Dreq. mm Dprov.

mm Ast mm2 Bar Dia. & Spacing

6 72 161.51 200 1130.09 Φ10 @70mm

8 73.5 163.19 300 1736.00 Φ12 @65mm

10 67.5 156.39 350 552.52 Φ16 @150mm

12 81 171.31 450 510.83 Φ20 @150mm

15 101.25 191.53 550 520.35 Φ25 @150mm

The counter forts act as self-supporting structural elements for retaining wall. It takes reactions, both from the stem as well as

Heel slab. The counter fort may be considered to bend as a cantilever, fixed at heel slab. The counter fort acts as an inverted T

beam of varying rib depth. The structural analysis of counter fort is done based on above assumptions. The Max. Depth of this

cantilever beam is width of heel slab. The steel reinforcement is provided as per requirement for tensile stress induced in it due to soil load on stem.

The moments and connection of counter fort details for various wall heights are as shown in table 10

Table 10: Moment and Connections of counter fort with Heel slab

Stamm. Moment Bar Dia. And Spacing

Connections of counter fort with Heel Slab

Horizontal Force Bar

Dia.

Spacing of

Stirrups

6 864 Φ20 @100mm 144 Φ8 100mm

8 1792 Φ20 @100mm 168 Φ8 100mm

10 3000 Φ25 @100mm 180 Φ10 100mm

12 5184 Φ25 @100mm 216 Φ10

100mm

15 10125 Φ32 @100mm 270 Φ12

100mm


_______________________________________________________________________________________


The main stress along counter fort is tensile. The connection of counter fort with base slab and stem is important for all assumed

mechanism. The steel reinforcement provided is in the form of two legged stirrups of required diameter steel. The saving in steel

reinforcement can be done as per curtailment / Reduction in number of stirrups from bottom to top side of wall.

3.2 Stepped Cantilever Retaining Wall

The stepped cantilever wall is new type suggested in this thesis. Here concrete steps are provided on stem projecting into backfill.

The pressure compacted backfill will anchor the concrete plate/step and will develop frictional resistance force; this will act as

indirect support for cantilever retaining wall. In short stem will act as propped cantilever and thus will reduce the destructive forces on stem / retaining wall.

Table 11: Summary of Dimensions of Stepped Cantilever Retaining Wall

Ht. of wall m

Total

base

slab

m

Width of Toe

Slab

M

Width of

Heel slab m

Base slab

Thk.

m

Stem Thickness

Top Bot

6 2.85 0.65 1.9 0.4 0.2 0.3

8 5.25 0.95 3.9 0.4 0.2 0.4

10 6.5 1.5 4.4 0.60 0.25 0.6

12 8.5 1.65 6.2 0.65 0.3 0.65

15 10.5 2.0 7.3 0.9 0.5 1.2

Concrete Steps

Total Spacing From

Top

Width

m

Depth

m

3.5 2 4.00 0.45 0.3

4.5 2 6.0 0.45 0.5

6.0 2 8 0.6 0.5

6.0 1.5 8 0.6 0.65

5.75 1.25 7.75 0.75 0.7

There is reduced soil load on base slab of wall firstly due to decreased base slab width and secondly due to reduction in load of soil resting on concrete steps/plates in backfill. In this case of wall interestingly it was the case that, wall was stable at shorter

dimensions but the stem was pulled inside backfill due to assumed frictional force hence the structural dimensions were not much

reduced to keep balance between self weight and resisting forces.

The forces acting and analysis and design of base slab for this new stepped cantilever retaining wall are as shown in Table12

Table 12: Structural Analysis of Stepped cantilever Retaining wall (Base slab)

Ht. Of wall m.

Bending moment (KNm)

Thickness Required

mm

Thickness Provided

Mm Toe Heel

6 72.03 105.00 195.05 400

8 205.34 800.88 538.68 650

10 581.84 987.57 598.18 750

12 656.00 1112.92 618.55 800

15 979.98 1553.13 750.15 900

Table 13: Design of Base slab of Stepped cantilever Retaining wall

Ht. of

wall

m.

Base slab

Thick.

Mm

Main Steel.

Toe slab Heel slab

Ast. mm2 Bar Dia. & Spacing Ast. mm2 Bar Dia. & Spacing

6 400 505.63 ϕ12

@150mm 741.68

Φ16

@150mm


_______________________________________________________________________________________


8 650 887.99 Φ20

@150mm 3623.94 ϕ25 @135mm

10 750 2217.81 Φ25

@150mm 3854.36 Φ32 @150mm

12 800 2343.51 Φ25

@150mm 4069.80

Φ25

@150mm

15 900 3130.30 Φ32

@150mm 5079.49

Φ36

@150mm

Ast.

mm2

960 1560 1800 1920 2160

Bar Dia.

& Spacing

Φ10

@80mm

Φ12

@75mm

Φ16

@100mm

Φ16

@100mm

Φ16

@90mm

The R.C.C. steps / plates projecting in backfill are main key elements in this type of wall. The Resisting force developed due to

these steps is function of depth of these steps below top of wall, surface roughness of concrete plates, degree of compaction of

backfill and specific weight of backfill. The steps are developing frictional force due to their anchorage in backfill and steps are

reinforced with sufficient steel required for tensile stress developed in it due to pulling effect. Though these steps are standing as

free cantilever in backfill, they will not be designed as cantilever as it is assumed as backfill is compacted.

The details of forces acting and design of these concrete steps is as shown in Table 14

Table 14: Concrete Step analysis and design details

Ht. of wall

m

Step

Dimensions

Location

Width Depth Depth below

Top

In Fill

Embedment

6 0.4 0.3 4.0 3.5

8 0.5 0.3 5.5 4.5

10 0.6 0.3 6.5 5.5

12 0.65 0.4 7.5 6.5

15 0.7 0.45 9.5 7.5

Reinforcement

Details Step spacing along

length

Frictional

force

developed Dia No

12 4 2.0 67.68

12 6 2.0 151.47

12 8 2.0 244.30

12 12 1.5 342.23

16 10 1.25 517.10

In this type of wall the nature of moment variation will be similar as that of Cantilever retaining wall but there will be drastic

change in moment at the point where concrete step is projected inside backfill. Up to this point the moment will be function of

height of backfill but below this the moment will be algebraic sum of both resisting and destructive moments i.e. Destructive

moment due to backfill and resisting moment of frictional force developed due to step.

The steel reinforcement will be provided not only adhering to moment values but with also consideration to minimum steel

quantities and Practical site considerations also.

The table 15 and 16 shows the moment variation and steel reinforcement provided for this stepped cantilever wall


_______________________________________________________________________________________


Table 15: Moment Variation Along length of stem for Stepped cantilever Wall

6m 8m 10m

Moment

KNm

D Prod

Mm

Moment

KNm

D Prod

mm

Moment

KNm

D Prod

mm

0-L/4 3.375 225 8.0 250 15.63 300

L/4-L/2 27.0 250 64.0 300 125 400

L/2-2L/3 91.12 275 216.0 450 421.87 600

2L/3-L 35.52 300 310.04 550 674.27 750

12m 15m

Moment

KNm

D Prod

mm

Moment

KNm

D Prod

Mm

0-L/4 27.0 350 52.7 400

L/4-L/2 216.0 500 421.9 700

L/2-2L/3 729 750 1423.8 1000

2L/3-L 1385.77 1000 2944.08 1400

Table 16: Reinforcement details along Height of stem

Ht. of

wall

m.

Moment Variation along

length of stem(KNm)

Steel prov. In Vertical wall

Stem Thickness

Dreq. Mm Dprov. Mm Ast mm2 Bar Dia. & Spacing

6 35.52 138.94 300 500.82 Φ12

@150mm 8 310.04 410.49 500 2732.36 Φ20 @115mm

10 674.27 605.35 700 4274.66 Φ25 @115mm

12 1385.77 867.83 950 4238.38 Φ25 @115mm

15 2944.08 1264.93 1350 9803.36 Φ32 @80mm

3.3 Unit Cost per Meter of Wall

A) Counter fort Retaining Wall:

The cost of counter fort retaining wall includes cost of concrete for stem, counter fort and base slab is added, and the steel quantity

is calculated from actual steel used with some provision for wastage also. For counter fort retaining wall, the cost of wall is

calculated for total spacing of counter forts and from this per meter cost of wall is calculated.

The cost per running meter for counter fort retaining wall for various retain heights is as shown in table

Table 17: Cost per Running Meter for Counter fort Retaining

Ht. of wall 6m 8m

Location Concretem3 Steel kg Concretem3 Steel kg

Stem 1.2 76.08 2.4 137.6

Base slab 0.98 66.16 1.49 80.08

Counter

Forts 2.7 137.2 5.18 234.05

Total 4.88 279.44 9.07 451.73

Rate 3500 43 3500 43

Amount 17080 12015.9 31745 19424.39

Sum 29095.9 51169.4

29100 51170


_______________________________________________________________________________________


10m 12m 15m

Concretem3 Steel kg Concretem3 Steel kg Concretem3 Steel kg

3.5 156.8 5.4 251.52 8.25 439.7

2.52 139.86 3.9 229.82 7.7 475.28

8.5 527.98 16.34 765.5 27.64 1810.55

14.52 824.64 25.64 1246.84 43.59 2725.53

3500 43 3500 43 3500 43

50820 35459.52 89740 53614.12 152565 117197.79

86279.52 143354.1 269763

86280 143360 269770

B) Stepped Cantilever Retaining Wall:

As like for counter fort retaining wall, the cost of stepped cantilever retaining wall will be calculated firstly as per spacing of steps

in backfill along length of wall and hence it is transferred to per meter cost. The construction practice for stepped cantilever wall

will not be very special than cantilever wall hence except extra amount for backfill compaction, no any extra provision is made in

cost calculation.

Table 18: Cost per running meter for Stepped Cantilever Retaining Wall

Ht. of

wall 6m 8m

Location Concretem3 Steel kg Concretem3 Steel kg

Stem 3 142.78 4.8 476.72

Base slab 2.28 84.91 4.2 370.71

Steps 0.25 8.2 0.39 16.63

Total 5.53 235.89 9.39 864.06

Rate 3500 43 3500 43

Amount 19355 10143.3 32865 37154.58

Sum 29498.3 70019.58

29500 70000

10m 12m 15m

Concretem3 Steel kg Concretem3 Steel

kg Concretem3 Steel kg

8.6 972.2 11.52 602.65 25.5 1688.23

7.8 623.21 8.29 500 11.8 850.07

0.55 26.18 0.9 59.69 1.2 100.88

16.95 1621.59 20.71 1162.3 38.5 2639.18

3500 43 3500 43 3500 43

59325 69728.4 72485 49981 134750 113485

129053 122466 248235

129050 122470 248240

3.5 Cost Comparison:

The cost per meter for all these three proposed types is tabulated above. In table 6.19 the comparison of concrete quantity per

meter for different wall heights and different wall types are shown.


_______________________________________________________________________________________


Table 19: Comparison of Concrete for Different Walls

Wall Ht.

m

Counter

fort wall

Stepped

Cantilever

wall

6 4.88 5.53

8 9.07 9.39

10 14.52 16.95

12 25.64 20.72

15 43.59 38.5

Graph15: Concrete Quantity Comparison

Table 20: Steel reinforcement per meter of wall

Wall Ht.

m Counter fort wall

Stepped Cantilever

wall

6 279.44 235.89

8 451.73 864.96

10 824.64 1621.59

12 1246.84 1162.34

15 2725.53 2639.18

Graph 16: Reinforcement Quantity Comparison


_______________________________________________________________________________________


The table 21 shows final cost comparison of all these wall types for same heights and graph 17 showing variation.

Table 21: Final Cost Comparison

Wall Ht.

m

Counter fort

wall

Stepped

Cantilever wall

6 29100 29500

8 51170 70000

10 86280 129050

12 143360 122470

15 269770 248240

Graph 17: Final Cost Comparison

It is clear from table that for heights from 8.0 M to 10.0 M

counter fort retaining wall is giving economical results.

Hence counter fort wall is better alternative for retaining

heights up to 10.0 M. Other wall types may also be checked

depending on actual site conditions.

The stepped cantilever is giving best result for height more

than 10.0 M, from this height counter fort retaining walls are

being uneconomical.

5. CONCLUSION

Cantilever retaining walls are economically suited for wall

heights up to 6.0 M and hence for height up to 6.0 M, no other alternative is necessary.

Counter fort retaining walls are suitable for retaining wall

heights 8.0 M to 10.0 M for standard site conditions

assumed. The other types of wall may also be tried for

different site conditions.

At first instant, Stepped cantilever Retaining wall are

economically best suited for wall heights from 11.0 M to

15.0 M. this is proving to be better alternative for large wall

heights as more than 11.0 M. Its mechanism is proven and

used in many civil engineering structures.

REFERENCES

[1]. S.K Bhatia and R.M Baker, “Difference between

Cantilever and Gravity retaining walls under static

conditions”, Indian Geotechnical Journal, Vol.15, No.3,

May 1985.

[2]. Kaare Hoeg and Ramesh Murarka, “Probabilistic

Analysis and Design of a Retaining Wall”, Journal of Geotechnical Engineering Division, Vol.100, March 1994.

[3]. Swami Saran, “Displacement Dependent Earth Pressure

in Retaining Walls”, Indian Geotechnical Journal, Indian

Geotechnical Journal, Vol.20, July 1990.

[4]. Leo Cassagrande, “Comments on Conventional Design

of Retaining Structures”, Journal of the soil mechanics and

foundation division, ASCE,, Vol.99, Feb2003.

BIOGRAPHIES

Prof. Dr.Patil S.S., B.E(Civil), M.E (Civil

–Structures), Ph.D (B.U., Bangalore),

Chairman Indian Society of Structural

Engineers Solapur Local Centre, Professor & Head of Civil Engineering Department,

Walchand Institute of Technology, Ashok

Chowk Solapur. (M.S) INDIA.

Mr. Bagban Aamir A.R, B.E (Civil), M.E

(Civil – Structures), M.E Student of WIT Solapur (M.S) INDIA